Given $ m \angle MON = 7x - 75$, and $ m \angle LOM = 4x + 90$, find $m\angle LOM$. $O$ $L$ $N$ $M$
From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {4x + 90} + {7x - 75} = {180}$ Combine like terms: $ 11x + 15 = 180$ Subtract $15$ from both sides: $ 11x = 165$ Divide both sides by $11$ to find $x$ $ x = 15$ Substitute $15$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 4({15}) + 90$ Simplify: $ {m\angle LOM = 60 + 90}$ So ${m\angle LOM = 150}$.